"We either leave the European Union with a deal…or we leave with no deal which is possible but I think parliament makes that unlikely, or we don't leave at all which I think would produce a democratic as well as a constitutional crisis," Fox told BBC radio.
He added that he didn't believe that the country had changed its mind on Brexit.
According to him, the 11 April deadline for the EU election decision would help to focus minds in Parliament.
The UK-EU Brexit talks are in a deadlock as the UK parliament refused to support May's negotiated deal with the bloc. The European Union has agreed to grant the United Kingdom a delay to the original departure date of 29 March.
The United Kingdom has until 22 May if its parliament passes the withdrawal deal next week, and until 12 April if it does not. At the same time, the European Union indicated it would not reopen negotiations on the deal agreed with the UK government.